Dissecting the Physics of Basketball Bank Shots

Here’s the scenario: You’re a college basketball player and your team is down by one. You’ve got a trip to the NCAA men’s basketball tournament on the line, but the clock shows less than three seconds. After your teammate passes you the ball, you dribble twice, pump-fake the defender, and throw up a jumpshot that could win the game.

Now, do you shoot the ball straight at the rim or aim for the backboard? According to researchers at North Carolina State, you better try to bank it in.

After analyzing computer-generated 3-D simulations of more than 1 million basketball shots, a team led by NC State’s Larry Silverberg determined that, while it does vary, there are large, identifiable areas on the court where a bank shot can be up to 20 percent more successful than attempting a direct swish.

The findings, published in the most recent issue of the Journal of Quantitative Analysis in Sports, make several assumptions about the ball shooter, in order to keep the the results determined by the 3-D sims consistent. One was that the ball be released at a height of either six, seven, or eight feet off the floor — a fairly typical height, if perhaps a little conservative.

Also, a regulation men’s basketball with a 29.5-inch circumference and 22-ounce weight was used in the sim. (Women’s basketball uses a ball that’s an inch smaller and two ounces lighter.) Finally, the ball rotated out of the shooter’s hands with a backspin of 3 Hz (three revolutions per second).

What they uncovered (shown here) was that areas on the wing — between the free-throw area (most of that inner rectangle) and the outermost three-point line — contained pockets (shown in the bottom-most graphic) where a bank shot was much more likely to go in than with a direct shot.

Up top, you can see the area that had the success rate for bank shots. It makes sense that the percentage drops so low on the outer area since you have such little surface area of the backboard to utilize.

Below that, you see the hot spots for converting direct shots.

Finally, at the bottom, you can see the areas (denoted in red) that had the highest increase in success rate with bank shots over direct shots. Indeed, these areas are usually off to the side of the straight-away area, where you’re more likely to get a good angle at the backboard.

The NC State team also discovered that when they plotted the simulated shooter’ aim points, the resulting data created a V that could be used as a training device for teaching players where the most successful bank shots are aimed. The dots that comprise the bottom-most part of the V represent shots taken closer to the free-throw line. Dots higher up on the V were from shots taken farther out on the wing.

But perhaps an even greater finding was that there existed, 3.326 inches behind the backboard, a vertical axis line that could be used to aid shooters in knowing where to aim their bank shots.

It’s actually quite simple: Envision the V (as shown here) on an actual backboard. Then visualize a vertical bar that sits 3.326 inches behind the backboard. Wherever you see the two cross, that’s where you aim for a high-percentage bank shot.

The problem is, teaching players to shoot high-percentage bank shots — because science tells us they have a better chance of going on — runs counter to the basic fundamentals of hoopdom. We see the rim, we want to shoot the ball at the rim. Shooting nothing but bank shots goes against human instinct, but it can be taught.

With enough reps — hopefully not 10,000 hours worth — you could train your eye to launch the ball at some arbitrary point away from the rim. Provided that your release point, ball rotation and body momentum remain constant, aim point can certainly be adjusted, especially if science convinces us our chances of scoring will go up.